Are you dancing with the same partner all of the time? That could be part of the problem. When I find myself in the wrong spot, it is usually because I am being led (pulled) to the wrong spot by an erring partner. This is a difficult problem to fix!
Most good Lindy dancers (as followers) do not find it necessary to stay square with their lead the whole time. Some dancers face away from their partner as they come out of the closed hold, and resolve their position on the 7&8.
It is necessary, however, to stay square for the rest of the step. Another way to help with this is to concentrate on your arm placement: If your left arm is folded so that your forearm is very close to you, you won't be square. So, pay attention to how you are placing your arms, and for the most part, if your arms are correct, so is the rest of you!
Concerning the swivels on counts 1,2: Practice practice practice! That's the only way I know of to make them better. You can also get a lot out of watching more experienced dancers, and trying to imitate their footwork.
Good luck!
Lola

Raistlyn,
I think your two problems (not getting around in the 3&4 turn fast enough and not staying square with your partner) are related. The easiest way to stay square with your partner is to look at him! During practice, you can try keeping your eye on his throat (I don't know why, but that area seems to work best). Make sure you do this constantly so you are always square with him (except on the swingout in open position if you want to do some styling on the 7&8). If you are always square with your partner, you should turn WITH him during the turn and it should be at just the right speed.

***You said you've been dancing for about a year, so forgive me if I'm being too basic--especially since its so hard to understand EXACTLY what people mean in forums

--Tany

Trees are people too!
¡Viva los árboles!